cPanel has recently the Horde webmail application framework to version 3.1.7 which fixes the security issues .

It is safe to re-enable Horde Webmail if your cPanel version is: cPanel 11.18.3 or greater. You may check the cPanel version by logging into your WHM. After you have logged in, look in the upper right-hand corner of the screen. It will display a version which will look similar to: "WHM 11.15.0 cPanel 11.18.3-R21703" - if the version number listed after cPanel is 11.18.3 or higher, then it is safe to re-enable Horde. If it is listed as 11.18.2 or lower, then do not re-enable Horde until cPanel has been updated.

You may re-enable Horde in your WHM by going to Server Configuration -> Tweak Settings. Then look under the "Mail" header for the option that says "Horde Webmail". Check the box next to that and scroll down to the bottom of the page and click "Save". If your version is not 11.18.3 or greater, then you can update cPanel through WHM. Login to WHM, then select cPanel -> Upgrade to Latest Version -> Click to Upgrade